{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# What is the energy distribution of FRB 121102 bursts?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pylab as pl\n",
    "from scipy.optimize import curve_fit\n",
    "from scipy.misc import factorial\n",
    "import astropy.cosmology as cosmo\n",
    "import astropy.units as u\n",
    "import multiprocessing\n",
    "from contextlib import closing\n",
    "\n",
    "# optimization produces lots of warning that can be ignored\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Some useful functions and data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# reference values and functions\n",
    "en_s = lambda ld, s: s*1e-23 * (4*np.pi*ld**2) * 5e-3 * 1.024e9 # VLA S-band energy in erg, s in Jy, ld in cm\n",
    "plaw = lambda x, alpha, a: a*(x/x[0])**alpha  # given array x, return powerlaw relative to first entry\n",
    "\n",
    "co = cosmo.Planck15\n",
    "ld0 = co.luminosity_distance(0.193)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "fluence_aom = np.array([0.1, 0.1, 0.1, 0.2, 0.09, 0.06, 0.06, 0.9, 0.3, 0.2, 1.0]) # spitler et al 2014, 2016\n",
    "fluence_aop = np.array([0.09])  # scholz et al 2016\n",
    "fluence_gbt = np.array([0.2, 0.4, 0.2, 0.08, 0.6])  # scholz et al 2016\n",
    "\n",
    "bw_aom = 322e6\n",
    "bw_gbt = 600e6\n",
    "bw_aop = 600e6\n",
    "\n",
    "# both were pointed on axis, more or less\n",
    "beam_aom = 1\n",
    "beam_gbt = 1\n",
    "\n",
    "en_aom = np.sort(beam_aom * fluence_aom * 1e-3 * bw_aom * 1e-23 * (4*np.pi*ld0.to(u.cm).value**2))\n",
    "en_aop = np.sort(fluence_aop * 1e-3 * bw_aop * 1e-23 * (4*np.pi*ld0.to(u.cm).value**2))\n",
    "en_gbt = np.sort(beam_gbt * fluence_gbt * 1e-3 * bw_gbt * 1e-23 * (4*np.pi*ld0.to(u.cm).value**2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Input burst energy distribution from modeling in candidate_spectra.ipynb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# using burst widths and phasing at best location\n",
    "en0 = np.array([11.5, 97.5, 7.2, 3.1, 34.0, 3.7, 10.0, 6.9, 11.6])*1e38 \n",
    "en0.sort()\n",
    "cnt = np.arange(1,len(en0)+1)[::-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Play with modeling of powerlaw"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Powerlaw slope -1.0 and amplitude 10.0 (at L=4.0690791232e+38)\n",
      "Cumulative powerlaw slope -0.644204483908 and amplitude 9.36998515143 (at L=3.1e+38)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1122fdf90>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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X15dnz54B8Pfff/PgwQMiIiLo3r07S5YsoXz58kya9PJGxd9++62xBympihQpQu7cudm7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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11229da50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# chisq minimization\n",
    "\n",
    "fig = pl.figure(figsize=(8,4))\n",
    "ax = fig.add_subplot(111)\n",
    "pl.plot(np.log10(en0), np.log10(cnt), 'kx', label='Data')\n",
    "\n",
    "bins = np.logspace(np.log10(0.9*en0.min()), np.log10(10*en0.max()), 10)\n",
    "#bins = np.linspace(0.9*en0.min(), 1.1*en0.max(), 10)\n",
    "cnt0, edg0 = pl.histogram(en0, bins=bins)\n",
    "bins = np.array([(edg0[i+1] + edg0[i])/2. for i in range(len(edg0)-1)])\n",
    "poptc, pcovc = curve_fit(plaw, bins, cnt0, sigma=np.sqrt(cnt0), p0=(-1, 10))\n",
    "print('Powerlaw slope {0} and amplitude {1} (at L={2})'.format(poptc[0], poptc[1], bins[0]))\n",
    "pl.plot(np.log10(bins), np.log10(cnt0), 'ko')\n",
    "pl.plot(np.log10(bins), np.log10(plaw(bins, *poptc)), 'k-', label='Energy powerlaw index {0:.1f}'.format(poptc[0]))\n",
    "\n",
    "popt0, pcov0 = curve_fit(plaw, en0, cnt, sigma=np.sqrt(cnt), p0=(-1, 10))\n",
    "print('Cumulative powerlaw slope {0} and amplitude {1} (at L={2})'.format(popt0[0], popt0[1], en0[0]))\n",
    "pl.plot(np.log10(en0), np.log10(plaw(en0, *popt0)), 'k--', label='Cumulative index {0:.1f}'.format(popt0[0]))\n",
    "\n",
    "pl.xlabel('log E (erg)', fontsize=14)\n",
    "pl.ylabel('N and N($>$E))', fontsize=14)\n",
    "pl.xlim(38.3, 40.1)\n",
    "pl.ylim(-0.3, 1.1)\n",
    "xt = pl.setp(ax.get_xticklabels(), fontsize=14)\n",
    "yt = pl.setp(ax.get_yticklabels(), fontsize=14)\n",
    "ax.xaxis.set_tick_params(width=2, color='k')\n",
    "ax.yaxis.set_tick_params(width=2, color='k')\n",
    "pl.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Build and plot cumulative distributions and rates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "cnt_aom = np.arange(1,len(en_aom)+1)[::-1]\n",
    "cnt_gbt = np.arange(1,len(en_gbt)+1)[::-1]\n",
    "en_all = np.sort(np.concatenate( (en_aom, en_gbt, en_aop, en0) ))\n",
    "cnt_all = np.arange(1, len(en_all) + 1)[::-1]\n",
    "\n",
    "# gbt pointed at repeater so flux is ok\n",
    "# ao off, but less than factor of 2\n",
    "\n",
    "# emphasize obs not at same epoch\n",
    "\n",
    "time_gbt = 15.3 # hrs\n",
    "time_vla = 27. # fall 2016 campaign\n",
    "time_aom = 4. # Spitler et al"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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lLuvduzdly5a1Sjwi+6TnT+QZDw8P2rVrR7t27cxlWms+/vhj83DxmDFjSE1N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\nn4iIiEgUUfEnIiIiEkX+P9Pl2N4D77CrAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112291c90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = pl.figure(figsize=(10,6))\n",
    "ax = fig.add_subplot(111)\n",
    "pl.plot(en0, cnt/time_vla, 'k.-', label='VLA late-2016')\n",
    "pl.plot([3e38], [0.1], 'kv', ms=15, label='VLA early-2016')\n",
    "pl.plot(en_aom, cnt_aom/time_aom, 'k.--', label='Arecibo')\n",
    "pl.plot(en_gbt, cnt_gbt/time_gbt, 'k.:', label='GBT')\n",
    "#pl.plot(en_all, cnt_all, 'k.-', size=30)\n",
    "pl.loglog()\n",
    "#pl.xlim(elim, 1.1e40)\n",
    "#pl.ylim(0.5, 20)\n",
    "pl.xlabel('Energy (erg)', fontsize=16)\n",
    "pl.ylabel('R ($>$E; per hour)', fontsize=16)\n",
    "pl.legend(fontsize=16)\n",
    "xt = pl.setp(ax.get_xticklabels(), fontsize=14)\n",
    "yt = pl.setp(ax.get_yticklabels(), fontsize=14)\n",
    "ax.xaxis.set_tick_params(width=2, color='k')\n",
    "ax.yaxis.set_tick_params(width=2, color='k')\n",
    "fig.savefig('energy_disn.pdf', format='pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Modeling of cumulative energy distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(-1.1155778894472361, -0.70351758793969843, -0.4120603015075377)\n",
      "(0.15170351758793971, 0.30240703517587941, 0.57367336683417081)\n",
      "(2, 9)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x114b91a50>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ATwzVGlRrSNKy1aLnoVGERhEUClAooOU26ChBRwmvIyLsVMJOpa1UpTOs0RnW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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11228c090>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rate = lambda e, elim, alpha, a: a*(e/elim)**alpha\n",
    "\n",
    "def like(pars, e, elim, c):\n",
    "    alpha, a0 = pars\n",
    "    lam = rate(e, elim, alpha, a0)\n",
    "    return (lam**c) * np.exp(-lam)/factorial(c)\n",
    "\n",
    "alphas = np.linspace(-2, 0, 200)\n",
    "a0s = np.linspace(1e-3, 3, 200)\n",
    "earr = np.zeros(shape=(len(alphas), len(a0s)))\n",
    "extent = (a0s[0], a0s[-1], alphas[0], alphas[-1])\n",
    "\n",
    "elim = 0.9*en0.min()\n",
    "ens = en0\n",
    "cnts = cnt\n",
    "\n",
    "engrid = np.logspace(np.log10(elim), 80, 2000)\n",
    "cntgrid = np.zeros(len(engrid), dtype=int)\n",
    "\n",
    "for en in ens:\n",
    "    i = np.where(engrid > en)[0][0]\n",
    "    cntgrid[i] += 1\n",
    "\n",
    "for i in range(len(alphas)):\n",
    "    for j in range(len(a0s)):\n",
    "        earr[i,j] = np.prod(like((alphas[i], a0s[j]), engrid, elim, cntgrid))\n",
    "\n",
    "\n",
    "# 95% bounds\n",
    "palpha, pa0 = np.where(earr == earr.max())\n",
    "walphas, wa0s = np.where(earr > 0.32*earr.max())\n",
    "print(alphas[walphas].min(), alphas[palpha[0]], alphas[walphas].max())\n",
    "print(a0s[wa0s].min(), a0s[pa0[0]], a0s[wa0s].max())\n",
    "print(cntgrid.max(), cntgrid.sum())\n",
    "popt1 = (alphas[palpha[0]], a0s[pa0[0]])\n",
    "\n",
    "fig = pl.figure(figsize=(12,5))\n",
    "ax = fig.add_subplot(121)\n",
    "pl.imshow(earr, interpolation='nearest', origin='bottom', cmap='magma',\n",
    "          aspect='auto', extent=extent)\n",
    "\n",
    "ax = fig.add_subplot(122)\n",
    "pl.plot(ens, cnts, 'k.-')\n",
    "pl.plot(engrid, rate(engrid, elim, alphas[palpha[0]], a0s[pa0[0]])[::-1].cumsum()[::-1], 'k--')\n",
    "pl.loglog()\n",
    "pl.xlim(elim, 1.1e40)\n",
    "pl.ylim(0.5, 20)\n",
    "plaw(engrid, alphas[palpha[0]], a0s[pa0[0]]).sum()\n",
    "pl.xlabel('Energy (erg)')\n",
    "pl.ylabel('N ($>$E)')"
   ]
  }
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